Duh! Of course peace trumps fear. Anybody knows that if you are at peace you are not afraid. But, being at peace is hard to do when you are have reason to be afraid. Just ask the disciples. Jesus had just been crucified and now supposedly raised from the dead (though no one but Mary Magdalene had actually seen Him, and everybody knew that Jesus had cast 7 demons out of her and maybe one had come back). So, all bets are still off related to them being safe from the Jews. If Jesus couldn’t overcome their schemes, they (the disciples) surely wouldn’t be able to outfox them (the jewish leaders committed to stamping out all threats to their religious authority). It was not looking good.
That is, till Jesus appeared to them. He WAS alive (sorry Mary)! He showed them His hands and feet and He came bearing peace. Twice He bathes them with peace, and when the Prince of Peace bids you peace that brings peace. And then to top it off He breathes on them and they are indwelt by the Holy Spirit Who bears fruit in the life of the believer one of which is peace. Were they still afraid? Maybe? But with the courage of conquerors they move out from the locked doors of the upper room and changed the world. In their case the peace of God had overcome the fear of God’s calling on their life. The peace that Jesus had given them overcame (yea, overruled) their fear.